document.write( "Question 1161537: If P(X) = 0.54, P(Y) = 0.36 and P(X and Y) = 0.27, what is the value of P(X/Y)? Is it the same as P(Y/X)? \n" ); document.write( "

Algebra.Com's Answer #785127 by ikleyn(52852) $\"\"$ $\"About$

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document.write( "By the definition of the conditional probability,\r\n" );
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document.write( "    P(x | Y) =  P(X ∩ Y) / P(Y).\r\n" );
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document.write( "Substitute the given numbers and calculate\r\n" );
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document.write( "    P(X | Y) =  =  = 0.75.\r\n" );
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document.write( "From the other side,\r\n" );
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document.write( "    P(Y | X) =  =  = 0.5.\r\n" );
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document.write( "As you see from my calculations,  P(X | Y)  is NOT EQUAL to  P(Y | X).\r\n" );
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\n" ); document.write( "\n" ); document.write( "On conditional probability, see the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Conditional probability problems \r
\n" ); document.write( "\n" ); document.write( "    - Conditional probability problems REVISITED \r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-II in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic \"Solved problems on Probability\"
\n" ); document.write( "and \"Additional problems on Probability\". \r
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\n" ); document.write( "\n" ); document.write( "Save the link to this textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-II
\n" ); document.write( "https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "into your archive and use when it is needed.\r
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document.write( "For students, who learn the conditional probability for the first time in their life,\r\n" );
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document.write( "it is REALLY difficult to comprehend its meaning.\r\n" );
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document.write( "Imagine a standard Venn diagram as two intersected circles, having some common area.\r\n" );
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document.write( "Call these circles X and Y; then the common area is their intersection (X ∩ Y).\r\n" );
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document.write( "   +-------------------------------------------------------------------------------------------------------+\r\n" );
document.write( "   |   The conditional probability  P(X | Y)  is the ratio of the common area to the area of the circle Y. |\r\n" );
document.write( "   |                                                                                                       |\r\n" );
document.write( "   |   The conditional probability  P(Y | X)  is the ratio of the common area to the area of the circle X. |\r\n" );
document.write( "   +-------------------------------------------------------------------------------------------------------+\r\n" );
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document.write( "After this explanation, you know EVERYTHING on this conception.\r\n" );
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